Converting decimal to binary?

py2006

Hi folks,

I am working away on some questions that will no doubt come up in an exam next year.

The first is converting a decimal number to a binary number.

Lets say 221:

221/2 = 110 remainder = 1
110/2 = 55 remainder = 0
55/2 = 27 remainder = 1
27/2 = 13 remainder = 1
13/2 = 6 remainder = 1
6/2 = 3 remainder = 0
3/2 = 1 remainder = 1
1/2 = 1 remainder = ???

Now I know you reverse the numbers to get the binary but I am not sure what the first number is

?1011101

Help meeeeeeeeeeeeeeeeeeee!

stipey

I didn't read this fully but this might help...

http://en.wikipedia.org/wiki/Binary_numeral_system#Decimal

Noelie

if it's a odd decimal number the last digit must always be a '1'

py2006

Noelie wrote:

if it's a odd decimal number the last digit must always be a '1'

Ah I see! I went to a site that automatically converts them and it had a 1 there. I couldn't figure out why!

Thanks

py2006

What about the reverse? Binary to decimal?

1010100

Noelie

is that read left to right or right to left? i could never remember
but i make that out to be 21

py2006

Noelie wrote:

is that read left to right or right to left? i could never remember
but i make that out to be 21

I don't know! I was hoping you could tell me!

py2006

py2006 wrote:

I don't know! I was hoping you could tell me!

I think there answer is actually 84! not sure!

Noelie

well i'm reading it from the left as the lsb, but i could be wrong it's been years since i done any of this stuff.
the lsb is 1, then 2 then 4, every next bit represents twice the previous so you'd have
1 2 4 8 16 32 64 128 256 512
1 0 1 0 1 0 0
so you add 1 + 4 + 16 and get 21.

but if the 0 on the rigth is the lsb you get
1 2 4 8 16 32 64 128 256 512
0 0 1 0 1 0 1
which would be 4 + 16 + 64 = 84

py2006

py2006 wrote:

I don't know! I was hoping you could tell me!

I think there answer is actually 84! not sure!

Noelie

just looked about a little and it's read from right to left, so the lsb is 0, making 84 the correct answer

Smellyirishman

To go from binary to decimal

The far right digit it 2^0 or 1,
the one left to that is 2^1 or 2,
left of that is 2^2 or 4.
left of that is 2^3 or 8.
etc...

So, if you have 101 as your binary number then 2^0 is "on" and 2^2 is "on" so 1+4 = 5.

In your example, it's.... nm, check out Noelie's explaination. (I am pretty sure 2^0 is the rightmost bit)

vallo

A minor point but can't you check it on your calculator?
You can do binary, octal, dec, hex conversions on any decent calculator - even the Microsoft(R) calculator can do it.

py2006

vallo wrote:

A minor point but can't you check it on your calculator?
You can do binary, octal, dec, hex conversions on any decent calculator - even the Microsoft(R) calculator can do it.

Yes, but they can't be brought into the exam!

dingding

Try this game for practice.

http://forums.cisco.com/CertCom/game/binary_game_page.htm?site=celc

Cheers

Pherekydes

py2006 wrote:

Hi folks,

1/2 = 1 remainder = ???

(

1/2 = 0 remainder 1.

This is your one mistake. Bí cúramach!

Pherekydes

For binary to decimal conversion:

1011:

= 1*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0)

= 8 + 0 + 2 + 1

= 11


Start on the right. The first bit is two to the power of zero, the next one is two to the power of one and so on.

py2006

Thanks guys! does the symbol ^ mean to power of?

Pherekydes

py2006 wrote:

Thanks guys! does the symbol ^ mean to power of?

Yes.